论文标题

失控:通过消除控制状态减少概率模型

Out of Control: Reducing Probabilistic Models by Control-State Elimination

论文作者

Winkler, Tobias, Lehmann, Johannes, Katoen, Joost-Pieter

论文摘要

最先进的概率模型检查员对在高级编程形式主义(如棱镜建模语言)中定义的显式状态马尔可夫模型进行验证。通常,由这种类似程序的规格产生的低级模型表现出许多结构,例如重复的子图案。诸如概率分配最小化之类的已建立技术能够利用这些结构。但是,它们直接在显式状态模型上运行。另一方面,通过对高级程序进行推理来减少结构化状态空间的方法尚未得到太多研究。在本文中,我们提出了一种新的,简单且全自动的程序级技术,以减少马尔可夫的基础模型。我们的方法旨在计算程序控制流图中相邻位置的摘要行为,从而获得更少的“控制状态”的程序。这种降低立即反映在程序的操作语义中,从而实现了更有效的模型检查。一个关键的见解是,原则上,程序变量与有限域的每个(组合)可以扮演定义流程结构的程序计数器的作用。与大多数其他还原技术不同,我们的方法是属性定向的,并且自然支持未指定的模型参数。实验表明,我们的简单方法可在实际相关基准的情况下产生高达80%的状态空间。

State-of-the-art probabilistic model checkers perform verification on explicit-state Markov models defined in a high-level programming formalism like the PRISM modeling language. Typically, the low-level models resulting from such program-like specifications exhibit lots of structure such as repeating subpatterns. Established techniques like probabilistic bisimulation minimization are able to exploit these structures; however, they operate directly on the explicit-state model. On the other hand, methods for reducing structured state spaces by reasoning about the high-level program have not been investigated that much. In this paper, we present a new, simple, and fully automatic program-level technique to reduce the underlying Markov model. Our approach aims at computing the summary behavior of adjacent locations in the program's control-flow graph, thereby obtaining a program with fewer "control states". This reduction is immediately reflected in the program's operational semantics, enabling more efficient model checking. A key insight is that in principle, each (combination of) program variable(s) with finite domain can play the role of the program counter that defines the flow structure. Unlike most other reduction techniques, our approach is property-directed and naturally supports unspecified model parameters. Experiments demonstrate that our simple method yields state-space reductions of up to 80% on practically relevant benchmarks.

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